Skip to main content
Log in

E. Frola (1906–1962): An Attempt Towards an Axiomatic Theory of Elasticity

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

In a few papers published in the 1940's, the Italian mathematician Eugenio Frola (1906–1962) proposed an axiomatic formulation of the theory of linear elasticity as an autonomous branch of mathematics, and he sketched a program for the logical foundations of that mathematical theory. He gave only some general principles and a few hints, without obtaining any definite axiomatic structure in the sense of the fundamental work of W. Noll and C. Truesdell a few years later. Nevertheless, Frola's attempt of finding rigorous axiomatic foundations of classical elasticity must be acknowledged as a very first step in the right direction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. Frola, La teoria dell'elasticitá. Il Saggiatore 1 (1940) 74–80.

    Google Scholar 

  2. E. Frola, Sull'elasticitá non globalmente lineare. Principi e fondamenti delle teorie. Atti Accad. Sci. Torino 75 (1940) 531–540.

    MATH  MathSciNet  Google Scholar 

  3. F. Pastrone, Fisica matematica e meccanica razionale. In: S. Di Sieno, A. Guerraggio and P. Nastasi (eds), La Matematica Italiana dopo l'Unitá. Gli Anni tra le Due Guerre Mondiali. Marcos y Marcos, Milano (1998) pp. 381–504.

    Google Scholar 

  4. E. Frola, Scritti Metodologici, L. Geymonat (ed.). Giappichelli, Torino (1964).

    Google Scholar 

  5. L. Geymonat, Eugenio Frola. Atti Accad. Sci. Torino 151 (1961/62) 986–997.

    Google Scholar 

  6. E. Frola, Su di una generalizzazione dinamica del teorema di Betti diversa da quella di Lord Rayleigh. Rend. Accad. Lincei s. VI XXV (1937) 586–589.

    Google Scholar 

  7. E. Frola, Intorno al teorema di Colonnetti sui sistemi elasto-plastici. Acta Pont. Acad. Sci. 2(7) (1938) 61–71.

    MATH  Google Scholar 

  8. E. Frola, Il problema di Cauchy in grande e le equazioni alle derivate parziali lineari a coefficienti costanti. Rend. Accad. Lincei s. VI XXVII (1938) 518–524.

    Google Scholar 

  9. E. Trefftz, Ueber die Ableitung der Stabilitätskriterien des elastischen Gleichgewichtes aus der Elastizitätstheorie endlicher Deformationen. In: Verh. 3. Internat. Kongr. Techn. Mech. 3 (1931) 44–50.

    MATH  Google Scholar 

  10. C.A. Truesdell, The meaning of Betti's reciprocal theorem. J. Research of N.B.S. 67B (1963) 85–86.

    MathSciNet  Google Scholar 

  11. V.V. Novozhilov, Foundations of the Nonlinear Theory of Elasticity. Gostekhizdat, Moscow (1948) (English transl. by F. Bagemihl, H. Komm and W. Seidel, Graylock, Rochester, NY (1953)).

    Google Scholar 

  12. C.A. Truesdell and R.A. Toupin, The classical field theories. In: S. Flügge (ed.), Handbuch der Physik, Vol. III/1. Springer, Berlin (1960) pp. 226–793.

    Google Scholar 

  13. J. Casey and P.M. Naghdi, Physically nonlinear and related approximate theories of elasticity, and their invariance properties. Arch. Rational Mech. Anal. 76 (1981) 355–390.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. P.M. Naghdi and L. Vongsarnpigoon, Small strain accompanied by moderate rotation. Arch. Rational Mech. Anal. 80 (1982) 263–294.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. P. Cicala, Sulla stabilitá dell'equilibrio elastico. Atti Accad. Sci. Torino 75 (1940) 185–222.

    MATH  MathSciNet  Google Scholar 

  16. P. Cicala, ItSulla teoria non lineare dell'elasticitá. Atti Accad. Sci. Torino 76 (1940) 94–104.

    MathSciNet  Google Scholar 

  17. E. Frola, Su alcune questioni di elasticitá non lineare. Atti Accad. Sci. Torino 77 (1942) 258–262.

    MATH  MathSciNet  Google Scholar 

  18. E. Frola, Sui fondamenti logici della teoria dell'elasticitá, Atti del Centro di Studi Metodologici I (1948) 12–14.

    Google Scholar 

  19. L. Giacardi and C.S. Roero, L'ereditá del Centro di Studi Metodologici di Torino. In: Quaderni di Storia dell'Universitá di Torino, Vol. 2. (1998) pp. 289–356.

    Google Scholar 

  20. E. Frola and B. Leoni, Possibilitá di applicazione delle matematiche alle discipline economiche. Il Politico 20 (1955) 190–210.

    Google Scholar 

  21. C. Truesdell and W. Noll, The nonlinear field theories of mechanics. In: S. Flügge (ed.), Handbuch der Physik, Vol. III/3. Springer, Berlin (1965) pp. 1–602.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Caparrini, S., Pastrone, F. E. Frola (1906–1962): An Attempt Towards an Axiomatic Theory of Elasticity. Journal of Elasticity 72, 43–55 (2003). https://doi.org/10.1023/B:ELAS.0000018789.38763.09

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:ELAS.0000018789.38763.09

Navigation